The rule which should guide us in such cases is simple and obvious enough: that the aggregate testimony of our neighbours is subject to the same conditions as the testimony of any one of them.

He was the first to suggest that gravitation might be a manifestation of an underlying geometry. He was much interested too in universal algebra and elliptic functions his papers "Preliminary Sketch of Biquaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics. This paper was famously attacked by pragmatist philosopher William James in his "Will to Believe" lecture.

In his philosophical writings he coined the expression "mind-stuff". Building on the work of Hermann Grassmann he introduced what is now termed geometric algebra a special case of the Clifford algebra named in his honour with interesting applications in contemporary mathematical physics and geometry.